With the advances in digital technology, there has been increasing demand to transmit digital information from place to place efficiently at higher rates. However, non-ideal properties of the communication media limit the transmission rate. For example, in chip-to-chip communications for backplane, front plane, and main-frame/personal computer applications, digital data are transmitted through a printed circuit board (PCB) trace, which causes frequency dependent loss, C(f). This loss can be modeled in the manner described in A. J. Baker, “An Adaptive Equalizer for Serial Digital Video Rates to 400 Mb/s”, IEEE International Solid-State Circuits Conference Digest of Technical Papers, pp. 174-175, 1996, as:C(f)=e−[hs(1 +j)√{square root over (f)}+hdf ]l,   (1)where, hs is the skin-effect loss coefficient, hd is the dielectric loss coefficient, l is the length of the media, and f is the frequency.
Thus, digital transmission, over channels such as PCB traces or cables, suffers from attenuation limiting the transmission speed and cable length. To improve data communication quality for better Bit Error Rate (BER), 8B10B coding is commonly used today for baseband data communications. This coding has 25% overhead, i.e. if the data are transmitted at 1 Gbps, the actual information rate is 800 Mbps, thus further limiting the actual data throughput.
In addition to channel loss, crosstalk noise is also a dominant noise factor in the channel. Frequency dependent loss within the signal bandwidth causes inter-symbol-interference (ISI), which in turn causes errors in data recovery at the receiver. As a result, the transmission data rate and the transmission distance are limited. To increase the data transmission throughput without increasing the symbol rate, multi-level (higher order) signaling methods, like 4-PAM, (four level Pulse Amplitude Modulation) and 8-PAM, have been proposed and implemented, for example in R. Farjad-Rad, C.-K. K. Yang, M. Horowitz and T. H. Lee, “A 0.3 μm CMOS 8-Gb/s 4-PAM Serial Link Transceiver,” IEEE Journal of Solid-State Circuits, Vol. 35, pp. 757-764, May 2000; and in J. T. Stonick, G.-Y. Wei, J. L. Sonntag and D. K. Weinlader, “An Adaptive PAM-4 5-Gb/s Backplane Transceiver in 0.25 μm CMOS,” IEEE Journal of Solid-State Circuits, Vol. 38, pp. 436-443, March 2003.
For the same data throughput, 4-PAM transmits data at half the rate of ordinary binary signaling (2-PAM). This is advantageous since the channel loss is smaller at lower frequencies. However, 4-PAM schemes that employ symbols {±1, ±3} suffer from the increased energy due to symbols ±3, and from having to use three thresholds to separate the symbols. Specifically, 4-PAM requires an average energy that is five times as much as ordinary binary, which has a significant impact on detection. Furthermore, if the same maximum amplitude is maintained, the separation between adjacent symbol amplitudes in 4-PAM is ⅓ of binary signaling, which results about a 9.5 dB loss in symbol power. As a result, the multi-level schemes present a higher level of difficulty for clock and data recovery, and an improvement over binary signaling is not guaranteed since the data throughput depends on the channel. For these reasons, higher order signaling does not appear to be promising for many applications of communication at high data rates. Hence, it is desirable to search for schemes that are binary, yet can increase the transmission rate without expanding the bandwidth.